What is expand (2x^3+4xy^2+y^2)dx+(2xy+4x^2y)dy ?

The solution to expand (2x^3+4xy^2+y^2)dx+(2xy+4x^2y)dy is 2x^3dx+4xy^2dx+y^2dx+2xydy+4x^2ydy

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expand (2x^3+4xy^2+y^2)dx+(2xy+4x^2y)dy

expand

(2 x^{3} + 4 x y^{2} + y^{2}) d x + (2 x y + 4 x^{2} y) d y

2 x^{3} d x + 4 x y^{2} d x + y^{2} d x + 2 x y d y + 4 x^{2} y d y

Solution steps

(2 x^{3} + 4 x y^{2} + y^{2}) d x + (2 x y + 4 x^{2} y) d y

Expand

d x (2 x^{3} + 4 x y^{2} + y^{2}) : 2 x^{3} d x + 4 x y^{2} d x + y^{2} d x

= 2 x^{3} d x + 4 x y^{2} d x + y^{2} d x + (2 x y + 4 x^{2} y) d y

Expand

d y (2 x y + 4 x^{2} y) : 2 x y d y + 4 x^{2} y d y

= 2 x^{3} d x + 4 x y^{2} d x + y^{2} d x + 2 x y d y + 4 x^{2} y d y

(\frac{1}{3} + \frac{x}{2}) (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2})

(8 x^{3} - \frac{12}{x ^{3}}) (4 x^{2} - \frac{6}{x ^{4}})

(4 x - \frac{1}{2} y)^{4}

x (\frac{3 x}{4} + \frac{10 - 3 x}{2})

What is expand (2x^3+4xy^2+y^2)dx+(2xy+4x^2y)dy ?
The solution to expand (2x^3+4xy^2+y^2)dx+(2xy+4x^2y)dy is 2x^3dx+4xy^2dx+y^2dx+2xydy+4x^2ydy